OFFSET
0,14
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1,0,0,0,1).
FORMULA
Let M = {{0, 1, 0}, {0, 0, 1}, {-I, -1, 0}}, v(0) = {0, 1, 1}, and v(n) = M*v(n-1) then {a(n), a(n+1)} = {abs(Re( v(n)((1)) )), abs(Im( v(n)((1)) ))}.
G.f.: x^2*(1+x^2)*(1 - x^4 + x^7)/((1 - x^4 + x^6)*(1 - x^4 - x^6)). - Colin Barker, Jan 01 2013
MATHEMATICA
M = {{0, 1, 0}, {0, 0, 1}, {-I, -1, 0}}; v[0] = {0, 1, 1};
v[n_]:= v[n] = M.v[n-1];
Flatten[Table[{Abs[Re[v[n][[1]]]], Abs[Im[v[n][[1]]]]}, {n, 0, 40}]]
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 82);
[0, 0] cat Coefficients(R!( x^2*(1+x^2)*(1-x^4+x^7)/(1-2*x^4+x^8-x^12) )); // G. C. Greubel, Jul 08 2021
(Sage)
def A114775_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x^2*(1+x^2)*(1-x^4+x^7)/(1-2*x^4+x^8-x^12) ).list()
A114775_list(82) # G. C. Greubel, Jul 08 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Feb 21 2006
EXTENSIONS
New name from Colin Barker, Jan 01 2013
Edited by G. C. Greubel, Jul 08 2021
STATUS
approved